Related papers: The Chow form of a reciprocal linear space

Zonotopal algebra is the study of a family of pairs of dual vector spaces of multivariate polynomials that can be associated with a list of vectors X. It connects objects from combinatorics, geometry, and approximation theory. The origin of…

We study the Chow group of 1-cycles of the moduli space of semistable parabolic vector bundles of fixed rank, determinant and a generic weight over a nonsingular projective curve over $\mathbb{C}$ of genus at least 3. We show that, the Chow…

We study linear spaces of symmetric matrices whose reciprocal is also a linear space. These are Jordan algebras. We classify such algebras in low dimensions, and we study the associated Jordan loci in the Grassmannian.

We relate the geometry of curves to the notion of hyperbolicity in real algebraic geometry. A hyperbolic variety is a real algebraic variety that (in particular) admits a real fibered morphism to a projective space whose dimension is equal…

We construct a complex of toric varieties we call the quasisymmetric Grassmannian inside the Grassmannian of $r$-planes in $\mathbb{C}^n$. Each irreducible component is a positroid variety and an $S_n$ translate of a toric Richardson…

We compute a presentation for the integral Chow rings of the moduli stacks of degree $2$ maps from smooth rational curves to projective space $\mathbb{P}^r$, as a quotient of a three-variable polynomial ring. The relations as $r$ varies…

We introduce a certain compactification of the space of projective configurations i.e. orbits of the group $PGL(k)$ on the space of $n$ - tuples of points in $P^{k-1}$ in general position. This compactification differs considerably from…

The study of Chow varieties of decomposable forms lies at the confluence of algebraic geometry, commutative algebra, representation theory and combinatorics. There are many open questions about homological properties of Chow varieties and…

It is shown that existence of a global solution to a particular nonlinear system of second order partial differential equations on a complete connected Riemannian manifold has topological and geometric implications and that in the domain of…

Consider the moduli space M^0 of arrangements of n hyperplanes in general position in projective (r-1)-space. When r=2 the space has a compactification given by the moduli space of stable curves of genus 0 with n marked points. In higher…

For an algebraically closed field K with ch K \not = 2, we determine the Chow ring of the moduli space of holomorphic bundles on a projective plane with the structure group SO(n,K) and half the first Pontryagin index being equal to 1, each…

The Schwarz map of the hypergeometric differential equation is studied since the beginning of the last century. Its target is the complex projective line, the 2-sphere. This paper introduces the hyperbolic Schwarz map, whose target is the…

We study the compactification of the locus parametrizing lines with a fixed intersection to a given line, inside the moduli space of line arrangements in the projective plane constructed for weight one by Hacking-Keel-Tevelev and Alexeev…

Learning generalizable self-supervised graph representations for downstream tasks is challenging. To this end, Contrastive Learning (CL) has emerged as a leading approach. The embeddings of CL are arranged on a hypersphere where similarity…

Let X be an algebraic projective variety in {\bf P}^n. Denote by {\cal C}_{\lambda} the space of all effective cycles on X whose homology class is \lambda \in H_{2p} (X,{\bf Z}). It is easy to show that {\cal C}_{\lambda} is an algebraic…

Let $X$ be a cubic hypersurface in $\mathbb P^6$ or a hypersurface of degree greater than equal to $7$ in $\mathbb P^5$. In this note we try to understand, for a very general hyperplane section of $X$, the non-injectivity locus of the…

Zonotopal algebras, introduced by Postnikov--Shapiro--Shapiro, Ardila--Postnikov, and Holtz--Ron, show up in many different contexts, including approximation theory, representation theory, Donaldson--Thomas theory, and hypertoric geometry.…

This article gives an invariant representation of the curvature of a plane wave spacetime in terms of the Schwarzian of a curve in the Lagrangian Grassmannian. It develops a general theory of cross ratios and Schwarzians of curves in what…

In this paper, the generic intersection theory for difference varieties is presented. Precisely, the intersection of an irreducible difference variety of dimension $d > 0$ and order $h$ with a generic difference hypersurface of order $s$ is…

Let M_{P^k}(P^r, d) be the moduli space of unparameterized maps \mu:P^k -> P^r satisfying \mu^*(O(1))= O(d). M_{P^k}(P^r,d) is a quasi-projective variety, and, in case k=1, M_{P^1}(P^r,d) is the fundamental open cell of Kontsevich's space…